Known Limits

Well-known limits

Existing limits

$$\lim_{x\to 0} \frac{\sin x}{x} = 1$$

Proof hint

Squeeze theorem with $\sin \theta \cos \theta \lt \theta \lt \tan\theta$. $$

$$\lim_{x\to a} \frac{x^n - a^n}{x - a} = na^{n-1}$$ $$\lim_{x\to \infty} \bigg(1+\frac{a}{x}\bigg)^{bx} = e^{ab}$$ $$\forall x\in\mathbb{R}\;\; \lim_{n\to\infty}\frac{x^n}{n!}=0$$

Limits that DNE

$$\lim_{x\to \infty} \sin x$$ $$\lim_{x\to 0} \sin\bigg(\frac{1}{x}\bigg)$$

Indeterminate forms

• $\frac{0}{0}$
• $\frac{\infty}{\infty}$
• $\infty\cdot0$
• $\infty-\infty$
• $\infty^{0}$
• $0^0$
• $1^\infty$